Particle displacement
| Sound measurements | |
|---|---|
|
Characteristic
|
Symbols
|
| Sound pressure | p, SPL |
| Particle velocity | v, SVL |
| Particle displacement | δ |
| Sound intensity | I, SIL |
| Sound power | P, SWL |
| Sound energy | W |
| Sound energy density | w |
| Sound exposure | E, SEL |
| Acoustic impedance | Z |
| Speed of sound | c |
| Audio frequency | AF |
| Transmission loss | TL |
|
|
|
Particle displacement or displacement amplitude is a measurement of distance of the movement of a particle from its equilibrium position in a medium as it transmits a second wave. The SI unit of particle displacement is the metre (m). In most cases this is a longitudinal wave of pressure (such as sound), but it can also be a transverse wave, such as the vibration of a taut string. In the case of a sound wave travelling through air, the particle displacement is evident in the oscillations of air molecules with, and against, the direction in which the sound wave is travelling.
A particle of the medium undergoes displacement according to the particle velocity of the sound wave traveling through the medium, while the sound wave itself moves at the speed of sound, equal to 343 m/s in air at 20 °C.
Particle displacement, denoted δ, is given by
where v is the particle velocity.
The particle displacement of a progressive sine wave is given by
where
It follows that the particle velocity and the sound pressure along the direction of propagation of the sound wave x are given by
where
Taking the Laplace transforms of v and p with respect to time yields
Since , the amplitude of the specific acoustic impedance is given by
...
Wikipedia